The sigma orientation for analytic circle-equivariant elliptic cohomology.

Ando, Matthew

Displaying similar documents to “The sigma orientation for analytic circle-equivariant elliptic cohomology.”

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Generalized orbifold Euler characteristics of symmetric orbifolds and covering spaces.

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Mirror symmetry for concavex vector bundles on projective spaces.

Elezi, Artur (2003)

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User's guide to equivariant methods in combinatorics. II.

Živaljević, Rade T. (1998)

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On localization in holomorphic equivariant cohomology

Ugo Bruzzo, Vladimir Rubtsov (2012)

Open Mathematics

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We study a holomorphic equivariant cohomology built out of the Atiyah algebroid of an equivariant holomorphic vector bundle and prove a related localization formula. This encompasses various residue formulas in complex geometry, in particular we shall show that it contains as special cases Carrell-Liebermann’s and Feng-Ma’s residue formulas, and Baum-Bott’s formula for the zeroes of a meromorphic vector field.

Equivariant principal bundles for G–actions and G–connections

Indranil Biswas, S. Senthamarai Kannan, D. S. Nagaraj (2015)

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Given a complex manifold M equipped with an action of a group G, and a holomorphic principal H–bundle EH on M, we introduce the notion of a connection on EH along the action of G, which is called a G–connection. We show some relationship between the condition that EH admits a G–equivariant structure and the condition that EH admits a (flat) G–connection. The cases of bundles on homogeneous spaces and smooth toric varieties are discussed.

Equivariant $K$ -theory

Graeme Segal (1968)

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The quantization conjecture revisited.

Teleman, Constantin (2000)

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On the homotopy groups of some equivariant automorphism groups of spheres

Dieter Erle (1975)

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Equivariant cohomology of the skyrmion bundle

Gross, Christian

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The author constructs the gauged Skyrme model by introducing the skyrmion bundle as follows: instead of considering maps $U : M \to {SU}_{N_{F}}$ he thinks of the meson fields as of global sections in a bundle $B (M, {SU}_{N_{F}}, G) = P (M, G) \times_{G} {SU}_{N_{F}}$ . For calculations within the skyrmion bundle the author introduces by means of the so-called equivariant cohomology an analogue of the topological charge and the Wess-Zumino term. The final result of this paper is the following Theorem. For the skyrmion bundle with $N_{F} \leq 6$ , one has $H^{*} (E G \times_{G} {SU}_{N_{F}}) ≅ H^{*} {({SU}_{N_{F}})}^{G} ≅ S ({\underset{̲}{G}}^{*}) \otimes H^{*} ({SU}_{N_{F}}) ≅ H^{*} (B G) \otimes H^{*} ({SU}_{N_{F}}),$ where $E G (B G, G)$ is the universal...